A vacuum cleaner is used to remove dirt from a floor. The cleaner includes a base, a handle extending upward from the base, and front and rear wheels for wheeling the base over the floor. A user manually applies a forward or rearward force to the handle to propel the base forward or rearward. A drive assist assembly in the base rotates the rear wheels in a direction and at a speed that correspond respectively to the direction and magnitude of the force applied to the handle. The assembly thus assists the user in wheeling the base over the floor.